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-----------------------------------------------------------------------------
Statistic identifier: St000508
-----------------------------------------------------------------------------
Collection: Standard tableaux
-----------------------------------------------------------------------------
Description: Eigenvalues of the random-to-random operator acting on a simple module.
The simple module of the symmetric group indexed by a partition $\lambda$ has dimension equal to the number of standard tableaux of shape $\lambda$. Hence, the eigenvalues of any linear operator defined on this module can be indexed by standard tableaux of shape $\lambda$; this statistic gives all the eigenvalues of the operator acting on the module [1].
-----------------------------------------------------------------------------
References: [1] Dieker, A. B., Saliola, F. Spectral analysis of random-to-random Markov chains [[arXiv:1509.08580]]
[2] Eigenvalues of the random-to-random operator acting on the regular representation Eigenvalues of the random-to-random operator acting on the regular representation. [[St000500]]
[3] The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. [[St000046]]
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Code:
def diagonal_index_of_partition(la):
return sum((j - i) for (i, j) in la.cells())
def binomial_shifted_diagonal_index_of_partition(partition):
return binomial(partition.size() + 1, 2) + diagonal_index_of_partition(partition)
def is_desarrangement_tableau(t):
if t.size() == 0:
return True
descents = t.standard_descents()
ascents = [i for i in t.entries() if i not in descents]
return min(ascents) % 2 == 0
def r2r_statistic_on_standard_tableaux(t):
# remove 1 and rectify until we get a desarrangement tableau
s = copy(t)
while not is_desarrangement_tableau(s):
s = SkewTableau([[(i-1 if i > 1 else None) for i in row] for row in s])
s = StandardTableau(s.rectify())
b_t = binomial_shifted_diagonal_index_of_partition(t.shape())
b_s = binomial_shifted_diagonal_index_of_partition(s.shape())
return b_t - b_s
def statistic(t):
return r2r_statistic_on_standard_tableaux(t)
-----------------------------------------------------------------------------
Statistic values:
[[1,2]] => 4
[[1],[2]] => 0
[[1,2,3]] => 9
[[1,3],[2]] => 0
[[1,2],[3]] => 4
[[1],[2],[3]] => 1
[[1,2,3,4]] => 16
[[1,3,4],[2]] => 0
[[1,2,4],[3]] => 6
[[1,2,3],[4]] => 10
[[1,3],[2,4]] => 0
[[1,2],[3,4]] => 4
[[1,4],[2],[3]] => 2
[[1,3],[2],[4]] => 0
[[1,2],[3],[4]] => 6
[[1],[2],[3],[4]] => 0
[[1,2,3,4,5]] => 25
[[1,3,4,5],[2]] => 0
[[1,2,4,5],[3]] => 8
[[1,2,3,5],[4]] => 14
[[1,2,3,4],[5]] => 18
[[1,3,5],[2,4]] => 0
[[1,2,5],[3,4]] => 5
[[1,3,4],[2,5]] => 0
[[1,2,4],[3,5]] => 7
[[1,2,3],[4,5]] => 11
[[1,4,5],[2],[3]] => 3
[[1,3,5],[2],[4]] => 0
[[1,2,5],[3],[4]] => 9
[[1,3,4],[2],[5]] => 0
[[1,2,4],[3],[5]] => 7
[[1,2,3],[4],[5]] => 13
[[1,4],[2,5],[3]] => 3
[[1,3],[2,5],[4]] => 0
[[1,2],[3,5],[4]] => 7
[[1,3],[2,4],[5]] => 0
[[1,2],[3,4],[5]] => 5
[[1,5],[2],[3],[4]] => 0
[[1,4],[2],[3],[5]] => 2
[[1,3],[2],[4],[5]] => 0
[[1,2],[3],[4],[5]] => 6
[[1],[2],[3],[4],[5]] => 1
[[1,2,3,4,5,6]] => 36
[[1,3,4,5,6],[2]] => 0
[[1,2,4,5,6],[3]] => 10
[[1,2,3,5,6],[4]] => 18
[[1,2,3,4,6],[5]] => 24
[[1,2,3,4,5],[6]] => 28
[[1,3,5,6],[2,4]] => 0
[[1,2,5,6],[3,4]] => 6
[[1,3,4,6],[2,5]] => 0
[[1,2,4,6],[3,5]] => 9
[[1,2,3,6],[4,5]] => 14
[[1,3,4,5],[2,6]] => 0
[[1,2,4,5],[3,6]] => 9
[[1,2,3,5],[4,6]] => 16
[[1,2,3,4],[5,6]] => 20
[[1,4,5,6],[2],[3]] => 4
[[1,3,5,6],[2],[4]] => 0
[[1,2,5,6],[3],[4]] => 12
[[1,3,4,6],[2],[5]] => 0
[[1,2,4,6],[3],[5]] => 9
[[1,2,3,6],[4],[5]] => 18
[[1,3,4,5],[2],[6]] => 0
[[1,2,4,5],[3],[6]] => 9
[[1,2,3,5],[4],[6]] => 16
[[1,2,3,4],[5],[6]] => 22
[[1,3,5],[2,4,6]] => 0
[[1,2,5],[3,4,6]] => 7
[[1,3,4],[2,5,6]] => 0
[[1,2,4],[3,5,6]] => 7
[[1,2,3],[4,5,6]] => 12
[[1,4,6],[2,5],[3]] => 4
[[1,3,6],[2,5],[4]] => 0
[[1,2,6],[3,5],[4]] => 9
[[1,3,6],[2,4],[5]] => 0
[[1,2,6],[3,4],[5]] => 6
[[1,4,5],[2,6],[3]] => 4
[[1,3,5],[2,6],[4]] => 0
[[1,2,5],[3,6],[4]] => 11
[[1,3,4],[2,6],[5]] => 0
[[1,2,4],[3,6],[5]] => 8
[[1,2,3],[4,6],[5]] => 15
[[1,3,5],[2,4],[6]] => 0
[[1,2,5],[3,4],[6]] => 6
[[1,3,4],[2,5],[6]] => 0
[[1,2,4],[3,5],[6]] => 8
[[1,2,3],[4,5],[6]] => 13
[[1,5,6],[2],[3],[4]] => 0
[[1,4,6],[2],[3],[5]] => 3
[[1,3,6],[2],[4],[5]] => 0
[[1,2,6],[3],[4],[5]] => 8
[[1,4,5],[2],[3],[6]] => 3
[[1,3,5],[2],[4],[6]] => 0
[[1,2,5],[3],[4],[6]] => 10
[[1,3,4],[2],[5],[6]] => 0
[[1,2,4],[3],[5],[6]] => 8
[[1,2,3],[4],[5],[6]] => 14
[[1,4],[2,5],[3,6]] => 5
[[1,3],[2,5],[4,6]] => 0
[[1,2],[3,5],[4,6]] => 8
[[1,3],[2,4],[5,6]] => 0
[[1,2],[3,4],[5,6]] => 5
[[1,5],[2,6],[3],[4]] => 0
[[1,4],[2,6],[3],[5]] => 3
[[1,3],[2,6],[4],[5]] => 0
[[1,2],[3,6],[4],[5]] => 6
[[1,4],[2,5],[3],[6]] => 3
[[1,3],[2,5],[4],[6]] => 0
[[1,2],[3,5],[4],[6]] => 8
[[1,3],[2,4],[5],[6]] => 0
[[1,2],[3,4],[5],[6]] => 6
[[1,6],[2],[3],[4],[5]] => 2
[[1,5],[2],[3],[4],[6]] => 0
[[1,4],[2],[3],[5],[6]] => 2
[[1,3],[2],[4],[5],[6]] => 0
[[1,2],[3],[4],[5],[6]] => 8
[[1],[2],[3],[4],[5],[6]] => 0
[[1,2,3,4,5,6,7]] => 49
[[1,3,4,5,6,7],[2]] => 0
[[1,2,4,5,6,7],[3]] => 12
[[1,2,3,5,6,7],[4]] => 22
[[1,2,3,4,6,7],[5]] => 30
[[1,2,3,4,5,7],[6]] => 36
[[1,2,3,4,5,6],[7]] => 40
[[1,3,5,6,7],[2,4]] => 0
[[1,2,5,6,7],[3,4]] => 7
[[1,3,4,6,7],[2,5]] => 0
[[1,2,4,6,7],[3,5]] => 11
[[1,2,3,6,7],[4,5]] => 17
[[1,3,4,5,7],[2,6]] => 0
[[1,2,4,5,7],[3,6]] => 11
[[1,2,3,5,7],[4,6]] => 20
[[1,2,3,4,7],[5,6]] => 25
[[1,3,4,5,6],[2,7]] => 0
[[1,2,4,5,6],[3,7]] => 11
[[1,2,3,5,6],[4,7]] => 20
[[1,2,3,4,6],[5,7]] => 27
[[1,2,3,4,5],[6,7]] => 31
[[1,4,5,6,7],[2],[3]] => 5
[[1,3,5,6,7],[2],[4]] => 0
[[1,2,5,6,7],[3],[4]] => 15
[[1,3,4,6,7],[2],[5]] => 0
[[1,2,4,6,7],[3],[5]] => 11
[[1,2,3,6,7],[4],[5]] => 23
[[1,3,4,5,7],[2],[6]] => 0
[[1,2,4,5,7],[3],[6]] => 11
[[1,2,3,5,7],[4],[6]] => 20
[[1,2,3,4,7],[5],[6]] => 29
[[1,3,4,5,6],[2],[7]] => 0
[[1,2,4,5,6],[3],[7]] => 11
[[1,2,3,5,6],[4],[7]] => 20
[[1,2,3,4,6],[5],[7]] => 27
[[1,2,3,4,5],[6],[7]] => 33
[[1,3,5,7],[2,4,6]] => 0
[[1,2,5,7],[3,4,6]] => 8
[[1,3,4,7],[2,5,6]] => 0
[[1,2,4,7],[3,5,6]] => 8
[[1,2,3,7],[4,5,6]] => 14
[[1,3,5,6],[2,4,7]] => 0
[[1,2,5,6],[3,4,7]] => 8
[[1,3,4,6],[2,5,7]] => 0
[[1,2,4,6],[3,5,7]] => 10
[[1,2,3,6],[4,5,7]] => 17
[[1,3,4,5],[2,6,7]] => 0
[[1,2,4,5],[3,6,7]] => 10
[[1,2,3,5],[4,6,7]] => 17
[[1,2,3,4],[5,6,7]] => 22
[[1,4,6,7],[2,5],[3]] => 5
[[1,3,6,7],[2,5],[4]] => 0
[[1,2,6,7],[3,5],[4]] => 11
[[1,3,6,7],[2,4],[5]] => 0
[[1,2,6,7],[3,4],[5]] => 7
[[1,4,5,7],[2,6],[3]] => 5
[[1,3,5,7],[2,6],[4]] => 0
[[1,2,5,7],[3,6],[4]] => 14
[[1,3,4,7],[2,6],[5]] => 0
[[1,2,4,7],[3,6],[5]] => 10
[[1,2,3,7],[4,6],[5]] => 19
[[1,3,5,7],[2,4],[6]] => 0
[[1,2,5,7],[3,4],[6]] => 7
[[1,3,4,7],[2,5],[6]] => 0
[[1,2,4,7],[3,5],[6]] => 10
[[1,2,3,7],[4,5],[6]] => 16
[[1,4,5,6],[2,7],[3]] => 5
[[1,3,5,6],[2,7],[4]] => 0
[[1,2,5,6],[3,7],[4]] => 14
[[1,3,4,6],[2,7],[5]] => 0
[[1,2,4,6],[3,7],[5]] => 10
[[1,2,3,6],[4,7],[5]] => 21
[[1,3,4,5],[2,7],[6]] => 0
[[1,2,4,5],[3,7],[6]] => 10
[[1,2,3,5],[4,7],[6]] => 18
[[1,2,3,4],[5,7],[6]] => 25
[[1,3,5,6],[2,4],[7]] => 0
[[1,2,5,6],[3,4],[7]] => 7
[[1,3,4,6],[2,5],[7]] => 0
[[1,2,4,6],[3,5],[7]] => 10
[[1,2,3,6],[4,5],[7]] => 16
[[1,3,4,5],[2,6],[7]] => 0
[[1,2,4,5],[3,6],[7]] => 10
[[1,2,3,5],[4,6],[7]] => 18
[[1,2,3,4],[5,6],[7]] => 23
[[1,5,6,7],[2],[3],[4]] => 0
[[1,4,6,7],[2],[3],[5]] => 4
[[1,3,6,7],[2],[4],[5]] => 0
[[1,2,6,7],[3],[4],[5]] => 10
[[1,4,5,7],[2],[3],[6]] => 4
[[1,3,5,7],[2],[4],[6]] => 0
[[1,2,5,7],[3],[4],[6]] => 13
[[1,3,4,7],[2],[5],[6]] => 0
[[1,2,4,7],[3],[5],[6]] => 10
[[1,2,3,7],[4],[5],[6]] => 18
[[1,4,5,6],[2],[3],[7]] => 4
[[1,3,5,6],[2],[4],[7]] => 0
[[1,2,5,6],[3],[4],[7]] => 13
[[1,3,4,6],[2],[5],[7]] => 0
[[1,2,4,6],[3],[5],[7]] => 10
[[1,2,3,6],[4],[5],[7]] => 20
[[1,3,4,5],[2],[6],[7]] => 0
[[1,2,4,5],[3],[6],[7]] => 10
[[1,2,3,5],[4],[6],[7]] => 18
[[1,2,3,4],[5],[6],[7]] => 24
[[1,4,6],[2,5,7],[3]] => 5
[[1,3,6],[2,5,7],[4]] => 0
[[1,2,6],[3,5,7],[4]] => 12
[[1,3,6],[2,4,7],[5]] => 0
[[1,2,6],[3,4,7],[5]] => 8
[[1,4,5],[2,6,7],[3]] => 5
[[1,3,5],[2,6,7],[4]] => 0
[[1,2,5],[3,6,7],[4]] => 12
[[1,3,4],[2,6,7],[5]] => 0
[[1,2,4],[3,6,7],[5]] => 8
[[1,2,3],[4,6,7],[5]] => 17
[[1,3,5],[2,4,7],[6]] => 0
[[1,2,5],[3,4,7],[6]] => 8
[[1,3,4],[2,5,7],[6]] => 0
[[1,2,4],[3,5,7],[6]] => 8
[[1,2,3],[4,5,7],[6]] => 14
[[1,3,5],[2,4,6],[7]] => 0
[[1,2,5],[3,4,6],[7]] => 8
[[1,3,4],[2,5,6],[7]] => 0
[[1,2,4],[3,5,6],[7]] => 8
[[1,2,3],[4,5,6],[7]] => 14
[[1,4,7],[2,5],[3,6]] => 6
[[1,3,7],[2,5],[4,6]] => 0
[[1,2,7],[3,5],[4,6]] => 10
[[1,3,7],[2,4],[5,6]] => 0
[[1,2,7],[3,4],[5,6]] => 6
[[1,4,6],[2,5],[3,7]] => 6
[[1,3,6],[2,5],[4,7]] => 0
[[1,2,6],[3,5],[4,7]] => 10
[[1,3,6],[2,4],[5,7]] => 0
[[1,2,6],[3,4],[5,7]] => 6
[[1,4,5],[2,6],[3,7]] => 6
[[1,3,5],[2,6],[4,7]] => 0
[[1,2,5],[3,6],[4,7]] => 14
[[1,3,4],[2,6],[5,7]] => 0
[[1,2,4],[3,6],[5,7]] => 9
[[1,2,3],[4,6],[5,7]] => 17
[[1,3,5],[2,4],[6,7]] => 0
[[1,2,5],[3,4],[6,7]] => 6
[[1,3,4],[2,5],[6,7]] => 0
[[1,2,4],[3,5],[6,7]] => 9
[[1,2,3],[4,5],[6,7]] => 14
[[1,5,7],[2,6],[3],[4]] => 0
[[1,4,7],[2,6],[3],[5]] => 4
[[1,3,7],[2,6],[4],[5]] => 0
[[1,2,7],[3,6],[4],[5]] => 7
[[1,4,7],[2,5],[3],[6]] => 4
[[1,3,7],[2,5],[4],[6]] => 0
[[1,2,7],[3,5],[4],[6]] => 10
[[1,3,7],[2,4],[5],[6]] => 0
[[1,2,7],[3,4],[5],[6]] => 7
[[1,5,6],[2,7],[3],[4]] => 0
[[1,4,6],[2,7],[3],[5]] => 4
[[1,3,6],[2,7],[4],[5]] => 0
[[1,2,6],[3,7],[4],[5]] => 9
[[1,4,5],[2,7],[3],[6]] => 4
[[1,3,5],[2,7],[4],[6]] => 0
[[1,2,5],[3,7],[4],[6]] => 12
[[1,3,4],[2,7],[5],[6]] => 0
[[1,2,4],[3,7],[5],[6]] => 9
[[1,2,3],[4,7],[5],[6]] => 15
[[1,4,6],[2,5],[3],[7]] => 4
[[1,3,6],[2,5],[4],[7]] => 0
[[1,2,6],[3,5],[4],[7]] => 10
[[1,3,6],[2,4],[5],[7]] => 0
[[1,2,6],[3,4],[5],[7]] => 7
[[1,4,5],[2,6],[3],[7]] => 4
[[1,3,5],[2,6],[4],[7]] => 0
[[1,2,5],[3,6],[4],[7]] => 12
[[1,3,4],[2,6],[5],[7]] => 0
[[1,2,4],[3,6],[5],[7]] => 9
[[1,2,3],[4,6],[5],[7]] => 17
[[1,3,5],[2,4],[6],[7]] => 0
[[1,2,5],[3,4],[6],[7]] => 7
[[1,3,4],[2,5],[6],[7]] => 0
[[1,2,4],[3,5],[6],[7]] => 9
[[1,2,3],[4,5],[6],[7]] => 15
[[1,6,7],[2],[3],[4],[5]] => 3
[[1,5,7],[2],[3],[4],[6]] => 0
[[1,4,7],[2],[3],[5],[6]] => 3
[[1,3,7],[2],[4],[5],[6]] => 0
[[1,2,7],[3],[4],[5],[6]] => 11
[[1,5,6],[2],[3],[4],[7]] => 0
[[1,4,6],[2],[3],[5],[7]] => 3
[[1,3,6],[2],[4],[5],[7]] => 0
[[1,2,6],[3],[4],[5],[7]] => 9
[[1,4,5],[2],[3],[6],[7]] => 3
[[1,3,5],[2],[4],[6],[7]] => 0
[[1,2,5],[3],[4],[6],[7]] => 11
[[1,3,4],[2],[5],[6],[7]] => 0
[[1,2,4],[3],[5],[6],[7]] => 9
[[1,2,3],[4],[5],[6],[7]] => 17
[[1,5],[2,6],[3,7],[4]] => 0
[[1,4],[2,6],[3,7],[5]] => 4
[[1,3],[2,6],[4,7],[5]] => 0
[[1,2],[3,6],[4,7],[5]] => 6
[[1,4],[2,5],[3,7],[6]] => 4
[[1,3],[2,5],[4,7],[6]] => 0
[[1,2],[3,5],[4,7],[6]] => 9
[[1,3],[2,4],[5,7],[6]] => 0
[[1,2],[3,4],[5,7],[6]] => 6
[[1,4],[2,5],[3,6],[7]] => 6
[[1,3],[2,5],[4,6],[7]] => 0
[[1,2],[3,5],[4,6],[7]] => 9
[[1,3],[2,4],[5,6],[7]] => 0
[[1,2],[3,4],[5,6],[7]] => 6
[[1,6],[2,7],[3],[4],[5]] => 3
[[1,5],[2,7],[3],[4],[6]] => 0
[[1,4],[2,7],[3],[5],[6]] => 3
[[1,3],[2,7],[4],[5],[6]] => 0
[[1,2],[3,7],[4],[5],[6]] => 9
[[1,5],[2,6],[3],[4],[7]] => 0
[[1,4],[2,6],[3],[5],[7]] => 3
[[1,3],[2,6],[4],[5],[7]] => 0
[[1,2],[3,6],[4],[5],[7]] => 7
[[1,4],[2,5],[3],[6],[7]] => 3
[[1,3],[2,5],[4],[6],[7]] => 0
[[1,2],[3,5],[4],[6],[7]] => 9
[[1,3],[2,4],[5],[6],[7]] => 0
[[1,2],[3,4],[5],[6],[7]] => 7
[[1,7],[2],[3],[4],[5],[6]] => 0
[[1,6],[2],[3],[4],[5],[7]] => 2
[[1,5],[2],[3],[4],[6],[7]] => 0
[[1,4],[2],[3],[5],[6],[7]] => 2
[[1,3],[2],[4],[5],[6],[7]] => 0
[[1,2],[3],[4],[5],[6],[7]] => 8
[[1],[2],[3],[4],[5],[6],[7]] => 1
[[1,2,3,4,5,6,7,8]] => 64
[[1,3,4,5,6,7,8],[2]] => 0
[[1,2,4,5,6,7,8],[3]] => 14
[[1,2,3,5,6,7,8],[4]] => 26
[[1,2,3,4,6,7,8],[5]] => 36
[[1,2,3,4,5,7,8],[6]] => 44
[[1,2,3,4,5,6,8],[7]] => 50
[[1,2,3,4,5,6,7],[8]] => 54
[[1,3,5,6,7,8],[2,4]] => 0
[[1,2,5,6,7,8],[3,4]] => 8
[[1,3,4,6,7,8],[2,5]] => 0
[[1,2,4,6,7,8],[3,5]] => 13
[[1,2,3,6,7,8],[4,5]] => 20
[[1,3,4,5,7,8],[2,6]] => 0
[[1,2,4,5,7,8],[3,6]] => 13
[[1,2,3,5,7,8],[4,6]] => 24
[[1,2,3,4,7,8],[5,6]] => 30
[[1,3,4,5,6,8],[2,7]] => 0
[[1,2,4,5,6,8],[3,7]] => 13
[[1,2,3,5,6,8],[4,7]] => 24
[[1,2,3,4,6,8],[5,7]] => 33
[[1,2,3,4,5,8],[6,7]] => 38
[[1,3,4,5,6,7],[2,8]] => 0
[[1,2,4,5,6,7],[3,8]] => 13
[[1,2,3,5,6,7],[4,8]] => 24
[[1,2,3,4,6,7],[5,8]] => 33
[[1,2,3,4,5,7],[6,8]] => 40
[[1,2,3,4,5,6],[7,8]] => 44
[[1,4,5,6,7,8],[2],[3]] => 6
[[1,3,5,6,7,8],[2],[4]] => 0
[[1,2,5,6,7,8],[3],[4]] => 18
[[1,3,4,6,7,8],[2],[5]] => 0
[[1,2,4,6,7,8],[3],[5]] => 13
[[1,2,3,6,7,8],[4],[5]] => 28
[[1,3,4,5,7,8],[2],[6]] => 0
[[1,2,4,5,7,8],[3],[6]] => 13
[[1,2,3,5,7,8],[4],[6]] => 24
[[1,2,3,4,7,8],[5],[6]] => 36
[[1,3,4,5,6,8],[2],[7]] => 0
[[1,2,4,5,6,8],[3],[7]] => 13
[[1,2,3,5,6,8],[4],[7]] => 24
[[1,2,3,4,6,8],[5],[7]] => 33
[[1,2,3,4,5,8],[6],[7]] => 42
[[1,3,4,5,6,7],[2],[8]] => 0
[[1,2,4,5,6,7],[3],[8]] => 13
[[1,2,3,5,6,7],[4],[8]] => 24
[[1,2,3,4,6,7],[5],[8]] => 33
[[1,2,3,4,5,7],[6],[8]] => 40
[[1,2,3,4,5,6],[7],[8]] => 46
[[1,3,5,7,8],[2,4,6]] => 0
[[1,2,5,7,8],[3,4,6]] => 9
[[1,3,4,7,8],[2,5,6]] => 0
[[1,2,4,7,8],[3,5,6]] => 9
[[1,2,3,7,8],[4,5,6]] => 16
[[1,3,5,6,8],[2,4,7]] => 0
[[1,2,5,6,8],[3,4,7]] => 9
[[1,3,4,6,8],[2,5,7]] => 0
[[1,2,4,6,8],[3,5,7]] => 12
[[1,2,3,6,8],[4,5,7]] => 20
[[1,3,4,5,8],[2,6,7]] => 0
[[1,2,4,5,8],[3,6,7]] => 12
[[1,2,3,5,8],[4,6,7]] => 20
[[1,2,3,4,8],[5,6,7]] => 26
[[1,3,5,6,7],[2,4,8]] => 0
[[1,2,5,6,7],[3,4,8]] => 9
[[1,3,4,6,7],[2,5,8]] => 0
[[1,2,4,6,7],[3,5,8]] => 12
[[1,2,3,6,7],[4,5,8]] => 20
[[1,3,4,5,7],[2,6,8]] => 0
[[1,2,4,5,7],[3,6,8]] => 12
[[1,2,3,5,7],[4,6,8]] => 22
[[1,2,3,4,7],[5,6,8]] => 29
[[1,3,4,5,6],[2,7,8]] => 0
[[1,2,4,5,6],[3,7,8]] => 12
[[1,2,3,5,6],[4,7,8]] => 22
[[1,2,3,4,6],[5,7,8]] => 29
[[1,2,3,4,5],[6,7,8]] => 34
[[1,4,6,7,8],[2,5],[3]] => 6
[[1,3,6,7,8],[2,5],[4]] => 0
[[1,2,6,7,8],[3,5],[4]] => 13
[[1,3,6,7,8],[2,4],[5]] => 0
[[1,2,6,7,8],[3,4],[5]] => 8
[[1,4,5,7,8],[2,6],[3]] => 6
[[1,3,5,7,8],[2,6],[4]] => 0
[[1,2,5,7,8],[3,6],[4]] => 17
[[1,3,4,7,8],[2,6],[5]] => 0
[[1,2,4,7,8],[3,6],[5]] => 12
[[1,2,3,7,8],[4,6],[5]] => 23
[[1,3,5,7,8],[2,4],[6]] => 0
[[1,2,5,7,8],[3,4],[6]] => 8
[[1,3,4,7,8],[2,5],[6]] => 0
[[1,2,4,7,8],[3,5],[6]] => 12
[[1,2,3,7,8],[4,5],[6]] => 19
[[1,4,5,6,8],[2,7],[3]] => 6
[[1,3,5,6,8],[2,7],[4]] => 0
[[1,2,5,6,8],[3,7],[4]] => 17
[[1,3,4,6,8],[2,7],[5]] => 0
[[1,2,4,6,8],[3,7],[5]] => 12
[[1,2,3,6,8],[4,7],[5]] => 26
[[1,3,4,5,8],[2,7],[6]] => 0
[[1,2,4,5,8],[3,7],[6]] => 12
[[1,2,3,5,8],[4,7],[6]] => 22
[[1,2,3,4,8],[5,7],[6]] => 31
[[1,3,5,6,8],[2,4],[7]] => 0
[[1,2,5,6,8],[3,4],[7]] => 8
[[1,3,4,6,8],[2,5],[7]] => 0
[[1,2,4,6,8],[3,5],[7]] => 12
[[1,2,3,6,8],[4,5],[7]] => 19
[[1,3,4,5,8],[2,6],[7]] => 0
[[1,2,4,5,8],[3,6],[7]] => 12
[[1,2,3,5,8],[4,6],[7]] => 22
[[1,2,3,4,8],[5,6],[7]] => 28
[[1,4,5,6,7],[2,8],[3]] => 6
[[1,3,5,6,7],[2,8],[4]] => 0
[[1,2,5,6,7],[3,8],[4]] => 17
[[1,3,4,6,7],[2,8],[5]] => 0
[[1,2,4,6,7],[3,8],[5]] => 12
[[1,2,3,6,7],[4,8],[5]] => 26
[[1,3,4,5,7],[2,8],[6]] => 0
[[1,2,4,5,7],[3,8],[6]] => 12
[[1,2,3,5,7],[4,8],[6]] => 22
[[1,2,3,4,7],[5,8],[6]] => 33
[[1,3,4,5,6],[2,8],[7]] => 0
[[1,2,4,5,6],[3,8],[7]] => 12
[[1,2,3,5,6],[4,8],[7]] => 22
[[1,2,3,4,6],[5,8],[7]] => 30
[[1,2,3,4,5],[6,8],[7]] => 37
[[1,3,5,6,7],[2,4],[8]] => 0
[[1,2,5,6,7],[3,4],[8]] => 8
[[1,3,4,6,7],[2,5],[8]] => 0
[[1,2,4,6,7],[3,5],[8]] => 12
[[1,2,3,6,7],[4,5],[8]] => 19
[[1,3,4,5,7],[2,6],[8]] => 0
[[1,2,4,5,7],[3,6],[8]] => 12
[[1,2,3,5,7],[4,6],[8]] => 22
[[1,2,3,4,7],[5,6],[8]] => 28
[[1,3,4,5,6],[2,7],[8]] => 0
[[1,2,4,5,6],[3,7],[8]] => 12
[[1,2,3,5,6],[4,7],[8]] => 22
[[1,2,3,4,6],[5,7],[8]] => 30
[[1,2,3,4,5],[6,7],[8]] => 35
[[1,5,6,7,8],[2],[3],[4]] => 0
[[1,4,6,7,8],[2],[3],[5]] => 5
[[1,3,6,7,8],[2],[4],[5]] => 0
[[1,2,6,7,8],[3],[4],[5]] => 12
[[1,4,5,7,8],[2],[3],[6]] => 5
[[1,3,5,7,8],[2],[4],[6]] => 0
[[1,2,5,7,8],[3],[4],[6]] => 16
[[1,3,4,7,8],[2],[5],[6]] => 0
[[1,2,4,7,8],[3],[5],[6]] => 12
[[1,2,3,7,8],[4],[5],[6]] => 22
[[1,4,5,6,8],[2],[3],[7]] => 5
[[1,3,5,6,8],[2],[4],[7]] => 0
[[1,2,5,6,8],[3],[4],[7]] => 16
[[1,3,4,6,8],[2],[5],[7]] => 0
[[1,2,4,6,8],[3],[5],[7]] => 12
[[1,2,3,6,8],[4],[5],[7]] => 25
[[1,3,4,5,8],[2],[6],[7]] => 0
[[1,2,4,5,8],[3],[6],[7]] => 12
[[1,2,3,5,8],[4],[6],[7]] => 22
[[1,2,3,4,8],[5],[6],[7]] => 30
[[1,4,5,6,7],[2],[3],[8]] => 5
[[1,3,5,6,7],[2],[4],[8]] => 0
[[1,2,5,6,7],[3],[4],[8]] => 16
[[1,3,4,6,7],[2],[5],[8]] => 0
[[1,2,4,6,7],[3],[5],[8]] => 12
[[1,2,3,6,7],[4],[5],[8]] => 25
[[1,3,4,5,7],[2],[6],[8]] => 0
[[1,2,4,5,7],[3],[6],[8]] => 12
[[1,2,3,5,7],[4],[6],[8]] => 22
[[1,2,3,4,7],[5],[6],[8]] => 32
[[1,3,4,5,6],[2],[7],[8]] => 0
[[1,2,4,5,6],[3],[7],[8]] => 12
[[1,2,3,5,6],[4],[7],[8]] => 22
[[1,2,3,4,6],[5],[7],[8]] => 30
[[1,2,3,4,5],[6],[7],[8]] => 36
[[1,3,5,7],[2,4,6,8]] => 0
[[1,2,5,7],[3,4,6,8]] => 10
[[1,3,4,7],[2,5,6,8]] => 0
[[1,2,4,7],[3,5,6,8]] => 10
[[1,2,3,7],[4,5,6,8]] => 18
[[1,3,5,6],[2,4,7,8]] => 0
[[1,2,5,6],[3,4,7,8]] => 10
[[1,3,4,6],[2,5,7,8]] => 0
[[1,2,4,6],[3,5,7,8]] => 10
[[1,2,3,6],[4,5,7,8]] => 18
[[1,3,4,5],[2,6,7,8]] => 0
[[1,2,4,5],[3,6,7,8]] => 10
[[1,2,3,5],[4,6,7,8]] => 18
[[1,2,3,4],[5,6,7,8]] => 24
[[1,4,6,8],[2,5,7],[3]] => 6
[[1,3,6,8],[2,5,7],[4]] => 0
[[1,2,6,8],[3,5,7],[4]] => 14
[[1,3,6,8],[2,4,7],[5]] => 0
[[1,2,6,8],[3,4,7],[5]] => 9
[[1,4,5,8],[2,6,7],[3]] => 6
[[1,3,5,8],[2,6,7],[4]] => 0
[[1,2,5,8],[3,6,7],[4]] => 14
[[1,3,4,8],[2,6,7],[5]] => 0
[[1,2,4,8],[3,6,7],[5]] => 9
[[1,2,3,8],[4,6,7],[5]] => 20
[[1,3,5,8],[2,4,7],[6]] => 0
[[1,2,5,8],[3,4,7],[6]] => 9
[[1,3,4,8],[2,5,7],[6]] => 0
[[1,2,4,8],[3,5,7],[6]] => 9
[[1,2,3,8],[4,5,7],[6]] => 16
[[1,3,5,8],[2,4,6],[7]] => 0
[[1,2,5,8],[3,4,6],[7]] => 9
[[1,3,4,8],[2,5,6],[7]] => 0
[[1,2,4,8],[3,5,6],[7]] => 9
[[1,2,3,8],[4,5,6],[7]] => 16
[[1,4,6,7],[2,5,8],[3]] => 6
[[1,3,6,7],[2,5,8],[4]] => 0
[[1,2,6,7],[3,5,8],[4]] => 14
[[1,3,6,7],[2,4,8],[5]] => 0
[[1,2,6,7],[3,4,8],[5]] => 9
[[1,4,5,7],[2,6,8],[3]] => 6
[[1,3,5,7],[2,6,8],[4]] => 0
[[1,2,5,7],[3,6,8],[4]] => 16
[[1,3,4,7],[2,6,8],[5]] => 0
[[1,2,4,7],[3,6,8],[5]] => 11
[[1,2,3,7],[4,6,8],[5]] => 23
[[1,3,5,7],[2,4,8],[6]] => 0
[[1,2,5,7],[3,4,8],[6]] => 9
[[1,3,4,7],[2,5,8],[6]] => 0
[[1,2,4,7],[3,5,8],[6]] => 11
[[1,2,3,7],[4,5,8],[6]] => 19
[[1,4,5,6],[2,7,8],[3]] => 6
[[1,3,5,6],[2,7,8],[4]] => 0
[[1,2,5,6],[3,7,8],[4]] => 16
[[1,3,4,6],[2,7,8],[5]] => 0
[[1,2,4,6],[3,7,8],[5]] => 11
[[1,2,3,6],[4,7,8],[5]] => 23
[[1,3,4,5],[2,7,8],[6]] => 0
[[1,2,4,5],[3,7,8],[6]] => 11
[[1,2,3,5],[4,7,8],[6]] => 19
[[1,2,3,4],[5,7,8],[6]] => 28
[[1,3,5,6],[2,4,8],[7]] => 0
[[1,2,5,6],[3,4,8],[7]] => 9
[[1,3,4,6],[2,5,8],[7]] => 0
[[1,2,4,6],[3,5,8],[7]] => 11
[[1,2,3,6],[4,5,8],[7]] => 19
[[1,3,4,5],[2,6,8],[7]] => 0
[[1,2,4,5],[3,6,8],[7]] => 11
[[1,2,3,5],[4,6,8],[7]] => 19
[[1,2,3,4],[5,6,8],[7]] => 25
[[1,3,5,7],[2,4,6],[8]] => 0
[[1,2,5,7],[3,4,6],[8]] => 9
[[1,3,4,7],[2,5,6],[8]] => 0
[[1,2,4,7],[3,5,6],[8]] => 9
[[1,2,3,7],[4,5,6],[8]] => 16
[[1,3,5,6],[2,4,7],[8]] => 0
[[1,2,5,6],[3,4,7],[8]] => 9
[[1,3,4,6],[2,5,7],[8]] => 0
[[1,2,4,6],[3,5,7],[8]] => 11
[[1,2,3,6],[4,5,7],[8]] => 19
[[1,3,4,5],[2,6,7],[8]] => 0
[[1,2,4,5],[3,6,7],[8]] => 11
[[1,2,3,5],[4,6,7],[8]] => 19
[[1,2,3,4],[5,6,7],[8]] => 25
[[1,4,7,8],[2,5],[3,6]] => 7
[[1,3,7,8],[2,5],[4,6]] => 0
[[1,2,7,8],[3,5],[4,6]] => 12
[[1,3,7,8],[2,4],[5,6]] => 0
[[1,2,7,8],[3,4],[5,6]] => 7
[[1,4,6,8],[2,5],[3,7]] => 7
[[1,3,6,8],[2,5],[4,7]] => 0
[[1,2,6,8],[3,5],[4,7]] => 12
[[1,3,6,8],[2,4],[5,7]] => 0
[[1,2,6,8],[3,4],[5,7]] => 7
[[1,4,5,8],[2,6],[3,7]] => 7
[[1,3,5,8],[2,6],[4,7]] => 0
[[1,2,5,8],[3,6],[4,7]] => 17
[[1,3,4,8],[2,6],[5,7]] => 0
[[1,2,4,8],[3,6],[5,7]] => 11
[[1,2,3,8],[4,6],[5,7]] => 21
[[1,3,5,8],[2,4],[6,7]] => 0
[[1,2,5,8],[3,4],[6,7]] => 7
[[1,3,4,8],[2,5],[6,7]] => 0
[[1,2,4,8],[3,5],[6,7]] => 11
[[1,2,3,8],[4,5],[6,7]] => 17
[[1,4,6,7],[2,5],[3,8]] => 7
[[1,3,6,7],[2,5],[4,8]] => 0
[[1,2,6,7],[3,5],[4,8]] => 12
[[1,3,6,7],[2,4],[5,8]] => 0
[[1,2,6,7],[3,4],[5,8]] => 7
[[1,4,5,7],[2,6],[3,8]] => 7
[[1,3,5,7],[2,6],[4,8]] => 0
[[1,2,5,7],[3,6],[4,8]] => 17
[[1,3,4,7],[2,6],[5,8]] => 0
[[1,2,4,7],[3,6],[5,8]] => 11
[[1,2,3,7],[4,6],[5,8]] => 21
[[1,3,5,7],[2,4],[6,8]] => 0
[[1,2,5,7],[3,4],[6,8]] => 7
[[1,3,4,7],[2,5],[6,8]] => 0
[[1,2,4,7],[3,5],[6,8]] => 11
[[1,2,3,7],[4,5],[6,8]] => 17
[[1,4,5,6],[2,7],[3,8]] => 7
[[1,3,5,6],[2,7],[4,8]] => 0
[[1,2,5,6],[3,7],[4,8]] => 17
[[1,3,4,6],[2,7],[5,8]] => 0
[[1,2,4,6],[3,7],[5,8]] => 11
[[1,2,3,6],[4,7],[5,8]] => 25
[[1,3,4,5],[2,7],[6,8]] => 0
[[1,2,4,5],[3,7],[6,8]] => 11
[[1,2,3,5],[4,7],[6,8]] => 20
[[1,2,3,4],[5,7],[6,8]] => 28
[[1,3,5,6],[2,4],[7,8]] => 0
[[1,2,5,6],[3,4],[7,8]] => 7
[[1,3,4,6],[2,5],[7,8]] => 0
[[1,2,4,6],[3,5],[7,8]] => 11
[[1,2,3,6],[4,5],[7,8]] => 17
[[1,3,4,5],[2,6],[7,8]] => 0
[[1,2,4,5],[3,6],[7,8]] => 11
[[1,2,3,5],[4,6],[7,8]] => 20
[[1,2,3,4],[5,6],[7,8]] => 25
[[1,5,7,8],[2,6],[3],[4]] => 0
[[1,4,7,8],[2,6],[3],[5]] => 5
[[1,3,7,8],[2,6],[4],[5]] => 0
[[1,2,7,8],[3,6],[4],[5]] => 8
[[1,4,7,8],[2,5],[3],[6]] => 5
[[1,3,7,8],[2,5],[4],[6]] => 0
[[1,2,7,8],[3,5],[4],[6]] => 12
[[1,3,7,8],[2,4],[5],[6]] => 0
[[1,2,7,8],[3,4],[5],[6]] => 8
[[1,5,6,8],[2,7],[3],[4]] => 0
[[1,4,6,8],[2,7],[3],[5]] => 5
[[1,3,6,8],[2,7],[4],[5]] => 0
[[1,2,6,8],[3,7],[4],[5]] => 11
[[1,4,5,8],[2,7],[3],[6]] => 5
[[1,3,5,8],[2,7],[4],[6]] => 0
[[1,2,5,8],[3,7],[4],[6]] => 15
[[1,3,4,8],[2,7],[5],[6]] => 0
[[1,2,4,8],[3,7],[5],[6]] => 11
[[1,2,3,8],[4,7],[5],[6]] => 18
[[1,4,6,8],[2,5],[3],[7]] => 5
[[1,3,6,8],[2,5],[4],[7]] => 0
[[1,2,6,8],[3,5],[4],[7]] => 12
[[1,3,6,8],[2,4],[5],[7]] => 0
[[1,2,6,8],[3,4],[5],[7]] => 8
[[1,4,5,8],[2,6],[3],[7]] => 5
[[1,3,5,8],[2,6],[4],[7]] => 0
[[1,2,5,8],[3,6],[4],[7]] => 15
[[1,3,4,8],[2,6],[5],[7]] => 0
[[1,2,4,8],[3,6],[5],[7]] => 11
[[1,2,3,8],[4,6],[5],[7]] => 21
[[1,3,5,8],[2,4],[6],[7]] => 0
[[1,2,5,8],[3,4],[6],[7]] => 8
[[1,3,4,8],[2,5],[6],[7]] => 0
[[1,2,4,8],[3,5],[6],[7]] => 11
[[1,2,3,8],[4,5],[6],[7]] => 18
[[1,5,6,7],[2,8],[3],[4]] => 0
[[1,4,6,7],[2,8],[3],[5]] => 5
[[1,3,6,7],[2,8],[4],[5]] => 0
[[1,2,6,7],[3,8],[4],[5]] => 11
[[1,4,5,7],[2,8],[3],[6]] => 5
[[1,3,5,7],[2,8],[4],[6]] => 0
[[1,2,5,7],[3,8],[4],[6]] => 15
[[1,3,4,7],[2,8],[5],[6]] => 0
[[1,2,4,7],[3,8],[5],[6]] => 11
[[1,2,3,7],[4,8],[5],[6]] => 20
[[1,4,5,6],[2,8],[3],[7]] => 5
[[1,3,5,6],[2,8],[4],[7]] => 0
[[1,2,5,6],[3,8],[4],[7]] => 15
[[1,3,4,6],[2,8],[5],[7]] => 0
[[1,2,4,6],[3,8],[5],[7]] => 11
[[1,2,3,6],[4,8],[5],[7]] => 23
[[1,3,4,5],[2,8],[6],[7]] => 0
[[1,2,4,5],[3,8],[6],[7]] => 11
[[1,2,3,5],[4,8],[6],[7]] => 20
[[1,2,3,4],[5,8],[6],[7]] => 26
[[1,4,6,7],[2,5],[3],[8]] => 5
[[1,3,6,7],[2,5],[4],[8]] => 0
[[1,2,6,7],[3,5],[4],[8]] => 12
[[1,3,6,7],[2,4],[5],[8]] => 0
[[1,2,6,7],[3,4],[5],[8]] => 8
[[1,4,5,7],[2,6],[3],[8]] => 5
[[1,3,5,7],[2,6],[4],[8]] => 0
[[1,2,5,7],[3,6],[4],[8]] => 15
[[1,3,4,7],[2,6],[5],[8]] => 0
[[1,2,4,7],[3,6],[5],[8]] => 11
[[1,2,3,7],[4,6],[5],[8]] => 21
[[1,3,5,7],[2,4],[6],[8]] => 0
[[1,2,5,7],[3,4],[6],[8]] => 8
[[1,3,4,7],[2,5],[6],[8]] => 0
[[1,2,4,7],[3,5],[6],[8]] => 11
[[1,2,3,7],[4,5],[6],[8]] => 18
[[1,4,5,6],[2,7],[3],[8]] => 5
[[1,3,5,6],[2,7],[4],[8]] => 0
[[1,2,5,6],[3,7],[4],[8]] => 15
[[1,3,4,6],[2,7],[5],[8]] => 0
[[1,2,4,6],[3,7],[5],[8]] => 11
[[1,2,3,6],[4,7],[5],[8]] => 23
[[1,3,4,5],[2,7],[6],[8]] => 0
[[1,2,4,5],[3,7],[6],[8]] => 11
[[1,2,3,5],[4,7],[6],[8]] => 20
[[1,2,3,4],[5,7],[6],[8]] => 28
[[1,3,5,6],[2,4],[7],[8]] => 0
[[1,2,5,6],[3,4],[7],[8]] => 8
[[1,3,4,6],[2,5],[7],[8]] => 0
[[1,2,4,6],[3,5],[7],[8]] => 11
[[1,2,3,6],[4,5],[7],[8]] => 18
[[1,3,4,5],[2,6],[7],[8]] => 0
[[1,2,4,5],[3,6],[7],[8]] => 11
[[1,2,3,5],[4,6],[7],[8]] => 20
[[1,2,3,4],[5,6],[7],[8]] => 26
[[1,6,7,8],[2],[3],[4],[5]] => 4
[[1,5,7,8],[2],[3],[4],[6]] => 0
[[1,4,7,8],[2],[3],[5],[6]] => 4
[[1,3,7,8],[2],[4],[5],[6]] => 0
[[1,2,7,8],[3],[4],[5],[6]] => 14
[[1,5,6,8],[2],[3],[4],[7]] => 0
[[1,4,6,8],[2],[3],[5],[7]] => 4
[[1,3,6,8],[2],[4],[5],[7]] => 0
[[1,2,6,8],[3],[4],[5],[7]] => 11
[[1,4,5,8],[2],[3],[6],[7]] => 4
[[1,3,5,8],[2],[4],[6],[7]] => 0
[[1,2,5,8],[3],[4],[6],[7]] => 14
[[1,3,4,8],[2],[5],[6],[7]] => 0
[[1,2,4,8],[3],[5],[6],[7]] => 11
[[1,2,3,8],[4],[5],[6],[7]] => 22
[[1,5,6,7],[2],[3],[4],[8]] => 0
[[1,4,6,7],[2],[3],[5],[8]] => 4
[[1,3,6,7],[2],[4],[5],[8]] => 0
[[1,2,6,7],[3],[4],[5],[8]] => 11
[[1,4,5,7],[2],[3],[6],[8]] => 4
[[1,3,5,7],[2],[4],[6],[8]] => 0
[[1,2,5,7],[3],[4],[6],[8]] => 14
[[1,3,4,7],[2],[5],[6],[8]] => 0
[[1,2,4,7],[3],[5],[6],[8]] => 11
[[1,2,3,7],[4],[5],[6],[8]] => 20
[[1,4,5,6],[2],[3],[7],[8]] => 4
[[1,3,5,6],[2],[4],[7],[8]] => 0
[[1,2,5,6],[3],[4],[7],[8]] => 14
[[1,3,4,6],[2],[5],[7],[8]] => 0
[[1,2,4,6],[3],[5],[7],[8]] => 11
[[1,2,3,6],[4],[5],[7],[8]] => 22
[[1,3,4,5],[2],[6],[7],[8]] => 0
[[1,2,4,5],[3],[6],[7],[8]] => 11
[[1,2,3,5],[4],[6],[7],[8]] => 20
[[1,2,3,4],[5],[6],[7],[8]] => 28
[[1,4,7],[2,5,8],[3,6]] => 7
[[1,3,7],[2,5,8],[4,6]] => 0
[[1,2,7],[3,5,8],[4,6]] => 12
[[1,3,7],[2,4,8],[5,6]] => 0
[[1,2,7],[3,4,8],[5,6]] => 7
[[1,4,6],[2,5,8],[3,7]] => 7
[[1,3,6],[2,5,8],[4,7]] => 0
[[1,2,6],[3,5,8],[4,7]] => 12
[[1,3,6],[2,4,8],[5,7]] => 0
[[1,2,6],[3,4,8],[5,7]] => 7
[[1,4,5],[2,6,8],[3,7]] => 7
[[1,3,5],[2,6,8],[4,7]] => 0
[[1,2,5],[3,6,8],[4,7]] => 15
[[1,3,4],[2,6,8],[5,7]] => 0
[[1,2,4],[3,6,8],[5,7]] => 9
[[1,2,3],[4,6,8],[5,7]] => 19
[[1,3,5],[2,4,8],[6,7]] => 0
[[1,2,5],[3,4,8],[6,7]] => 7
[[1,3,4],[2,5,8],[6,7]] => 0
[[1,2,4],[3,5,8],[6,7]] => 9
[[1,2,3],[4,5,8],[6,7]] => 15
[[1,4,6],[2,5,7],[3,8]] => 7
[[1,3,6],[2,5,7],[4,8]] => 0
[[1,2,6],[3,5,7],[4,8]] => 15
[[1,3,6],[2,4,7],[5,8]] => 0
[[1,2,6],[3,4,7],[5,8]] => 9
[[1,4,5],[2,6,7],[3,8]] => 7
[[1,3,5],[2,6,7],[4,8]] => 0
[[1,2,5],[3,6,7],[4,8]] => 15
[[1,3,4],[2,6,7],[5,8]] => 0
[[1,2,4],[3,6,7],[5,8]] => 9
[[1,2,3],[4,6,7],[5,8]] => 19
[[1,3,5],[2,4,7],[6,8]] => 0
[[1,2,5],[3,4,7],[6,8]] => 9
[[1,3,4],[2,5,7],[6,8]] => 0
[[1,2,4],[3,5,7],[6,8]] => 9
[[1,2,3],[4,5,7],[6,8]] => 15
[[1,3,5],[2,4,6],[7,8]] => 0
[[1,2,5],[3,4,6],[7,8]] => 9
[[1,3,4],[2,5,6],[7,8]] => 0
[[1,2,4],[3,5,6],[7,8]] => 9
[[1,2,3],[4,5,6],[7,8]] => 15
[[1,5,7],[2,6,8],[3],[4]] => 0
[[1,4,7],[2,6,8],[3],[5]] => 5
[[1,3,7],[2,6,8],[4],[5]] => 0
[[1,2,7],[3,6,8],[4],[5]] => 9
[[1,4,7],[2,5,8],[3],[6]] => 5
[[1,3,7],[2,5,8],[4],[6]] => 0
[[1,2,7],[3,5,8],[4],[6]] => 13
[[1,3,7],[2,4,8],[5],[6]] => 0
[[1,2,7],[3,4,8],[5],[6]] => 9
[[1,5,6],[2,7,8],[3],[4]] => 0
[[1,4,6],[2,7,8],[3],[5]] => 5
[[1,3,6],[2,7,8],[4],[5]] => 0
[[1,2,6],[3,7,8],[4],[5]] => 9
[[1,4,5],[2,7,8],[3],[6]] => 5
[[1,3,5],[2,7,8],[4],[6]] => 0
[[1,2,5],[3,7,8],[4],[6]] => 13
[[1,3,4],[2,7,8],[5],[6]] => 0
[[1,2,4],[3,7,8],[5],[6]] => 9
[[1,2,3],[4,7,8],[5],[6]] => 16
[[1,4,6],[2,5,8],[3],[7]] => 5
[[1,3,6],[2,5,8],[4],[7]] => 0
[[1,2,6],[3,5,8],[4],[7]] => 13
[[1,3,6],[2,4,8],[5],[7]] => 0
[[1,2,6],[3,4,8],[5],[7]] => 9
[[1,4,5],[2,6,8],[3],[7]] => 5
[[1,3,5],[2,6,8],[4],[7]] => 0
[[1,2,5],[3,6,8],[4],[7]] => 13
[[1,3,4],[2,6,8],[5],[7]] => 0
[[1,2,4],[3,6,8],[5],[7]] => 9
[[1,2,3],[4,6,8],[5],[7]] => 19
[[1,3,5],[2,4,8],[6],[7]] => 0
[[1,2,5],[3,4,8],[6],[7]] => 9
[[1,3,4],[2,5,8],[6],[7]] => 0
[[1,2,4],[3,5,8],[6],[7]] => 9
[[1,2,3],[4,5,8],[6],[7]] => 16
[[1,4,6],[2,5,7],[3],[8]] => 5
[[1,3,6],[2,5,7],[4],[8]] => 0
[[1,2,6],[3,5,7],[4],[8]] => 13
[[1,3,6],[2,4,7],[5],[8]] => 0
[[1,2,6],[3,4,7],[5],[8]] => 9
[[1,4,5],[2,6,7],[3],[8]] => 5
[[1,3,5],[2,6,7],[4],[8]] => 0
[[1,2,5],[3,6,7],[4],[8]] => 13
[[1,3,4],[2,6,7],[5],[8]] => 0
[[1,2,4],[3,6,7],[5],[8]] => 9
[[1,2,3],[4,6,7],[5],[8]] => 19
[[1,3,5],[2,4,7],[6],[8]] => 0
[[1,2,5],[3,4,7],[6],[8]] => 9
[[1,3,4],[2,5,7],[6],[8]] => 0
[[1,2,4],[3,5,7],[6],[8]] => 9
[[1,2,3],[4,5,7],[6],[8]] => 16
[[1,3,5],[2,4,6],[7],[8]] => 0
[[1,2,5],[3,4,6],[7],[8]] => 9
[[1,3,4],[2,5,6],[7],[8]] => 0
[[1,2,4],[3,5,6],[7],[8]] => 9
[[1,2,3],[4,5,6],[7],[8]] => 16
[[1,5,8],[2,6],[3,7],[4]] => 0
[[1,4,8],[2,6],[3,7],[5]] => 5
[[1,3,8],[2,6],[4,7],[5]] => 0
[[1,2,8],[3,6],[4,7],[5]] => 7
[[1,4,8],[2,5],[3,7],[6]] => 5
[[1,3,8],[2,5],[4,7],[6]] => 0
[[1,2,8],[3,5],[4,7],[6]] => 11
[[1,3,8],[2,4],[5,7],[6]] => 0
[[1,2,8],[3,4],[5,7],[6]] => 7
[[1,4,8],[2,5],[3,6],[7]] => 7
[[1,3,8],[2,5],[4,6],[7]] => 0
[[1,2,8],[3,5],[4,6],[7]] => 11
[[1,3,8],[2,4],[5,6],[7]] => 0
[[1,2,8],[3,4],[5,6],[7]] => 7
[[1,5,7],[2,6],[3,8],[4]] => 0
[[1,4,7],[2,6],[3,8],[5]] => 5
[[1,3,7],[2,6],[4,8],[5]] => 0
[[1,2,7],[3,6],[4,8],[5]] => 7
[[1,4,7],[2,5],[3,8],[6]] => 5
[[1,3,7],[2,5],[4,8],[6]] => 0
[[1,2,7],[3,5],[4,8],[6]] => 11
[[1,3,7],[2,4],[5,8],[6]] => 0
[[1,2,7],[3,4],[5,8],[6]] => 7
[[1,5,6],[2,7],[3,8],[4]] => 0
[[1,4,6],[2,7],[3,8],[5]] => 5
[[1,3,6],[2,7],[4,8],[5]] => 0
[[1,2,6],[3,7],[4,8],[5]] => 10
[[1,4,5],[2,7],[3,8],[6]] => 5
[[1,3,5],[2,7],[4,8],[6]] => 0
[[1,2,5],[3,7],[4,8],[6]] => 14
[[1,3,4],[2,7],[5,8],[6]] => 0
[[1,2,4],[3,7],[5,8],[6]] => 10
[[1,2,3],[4,7],[5,8],[6]] => 16
[[1,4,6],[2,5],[3,8],[7]] => 5
[[1,3,6],[2,5],[4,8],[7]] => 0
[[1,2,6],[3,5],[4,8],[7]] => 11
[[1,3,6],[2,4],[5,8],[7]] => 0
[[1,2,6],[3,4],[5,8],[7]] => 7
[[1,4,5],[2,6],[3,8],[7]] => 5
[[1,3,5],[2,6],[4,8],[7]] => 0
[[1,2,5],[3,6],[4,8],[7]] => 14
[[1,3,4],[2,6],[5,8],[7]] => 0
[[1,2,4],[3,6],[5,8],[7]] => 10
[[1,2,3],[4,6],[5,8],[7]] => 19
[[1,3,5],[2,4],[6,8],[7]] => 0
[[1,2,5],[3,4],[6,8],[7]] => 7
[[1,3,4],[2,5],[6,8],[7]] => 0
[[1,2,4],[3,5],[6,8],[7]] => 10
[[1,2,3],[4,5],[6,8],[7]] => 16
[[1,4,7],[2,5],[3,6],[8]] => 7
[[1,3,7],[2,5],[4,6],[8]] => 0
[[1,2,7],[3,5],[4,6],[8]] => 11
[[1,3,7],[2,4],[5,6],[8]] => 0
[[1,2,7],[3,4],[5,6],[8]] => 7
[[1,4,6],[2,5],[3,7],[8]] => 7
[[1,3,6],[2,5],[4,7],[8]] => 0
[[1,2,6],[3,5],[4,7],[8]] => 11
[[1,3,6],[2,4],[5,7],[8]] => 0
[[1,2,6],[3,4],[5,7],[8]] => 7
[[1,4,5],[2,6],[3,7],[8]] => 7
[[1,3,5],[2,6],[4,7],[8]] => 0
[[1,2,5],[3,6],[4,7],[8]] => 16
[[1,3,4],[2,6],[5,7],[8]] => 0
[[1,2,4],[3,6],[5,7],[8]] => 10
[[1,2,3],[4,6],[5,7],[8]] => 19
[[1,3,5],[2,4],[6,7],[8]] => 0
[[1,2,5],[3,4],[6,7],[8]] => 7
[[1,3,4],[2,5],[6,7],[8]] => 0
[[1,2,4],[3,5],[6,7],[8]] => 10
[[1,2,3],[4,5],[6,7],[8]] => 16
[[1,6,8],[2,7],[3],[4],[5]] => 4
[[1,5,8],[2,7],[3],[4],[6]] => 0
[[1,4,8],[2,7],[3],[5],[6]] => 4
[[1,3,8],[2,7],[4],[5],[6]] => 0
[[1,2,8],[3,7],[4],[5],[6]] => 11
[[1,5,8],[2,6],[3],[4],[7]] => 0
[[1,4,8],[2,6],[3],[5],[7]] => 4
[[1,3,8],[2,6],[4],[5],[7]] => 0
[[1,2,8],[3,6],[4],[5],[7]] => 8
[[1,4,8],[2,5],[3],[6],[7]] => 4
[[1,3,8],[2,5],[4],[6],[7]] => 0
[[1,2,8],[3,5],[4],[6],[7]] => 11
[[1,3,8],[2,4],[5],[6],[7]] => 0
[[1,2,8],[3,4],[5],[6],[7]] => 8
[[1,6,7],[2,8],[3],[4],[5]] => 4
[[1,5,7],[2,8],[3],[4],[6]] => 0
[[1,4,7],[2,8],[3],[5],[6]] => 4
[[1,3,7],[2,8],[4],[5],[6]] => 0
[[1,2,7],[3,8],[4],[5],[6]] => 13
[[1,5,6],[2,8],[3],[4],[7]] => 0
[[1,4,6],[2,8],[3],[5],[7]] => 4
[[1,3,6],[2,8],[4],[5],[7]] => 0
[[1,2,6],[3,8],[4],[5],[7]] => 10
[[1,4,5],[2,8],[3],[6],[7]] => 4
[[1,3,5],[2,8],[4],[6],[7]] => 0
[[1,2,5],[3,8],[4],[6],[7]] => 13
[[1,3,4],[2,8],[5],[6],[7]] => 0
[[1,2,4],[3,8],[5],[6],[7]] => 10
[[1,2,3],[4,8],[5],[6],[7]] => 19
[[1,5,7],[2,6],[3],[4],[8]] => 0
[[1,4,7],[2,6],[3],[5],[8]] => 4
[[1,3,7],[2,6],[4],[5],[8]] => 0
[[1,2,7],[3,6],[4],[5],[8]] => 8
[[1,4,7],[2,5],[3],[6],[8]] => 4
[[1,3,7],[2,5],[4],[6],[8]] => 0
[[1,2,7],[3,5],[4],[6],[8]] => 11
[[1,3,7],[2,4],[5],[6],[8]] => 0
[[1,2,7],[3,4],[5],[6],[8]] => 8
[[1,5,6],[2,7],[3],[4],[8]] => 0
[[1,4,6],[2,7],[3],[5],[8]] => 4
[[1,3,6],[2,7],[4],[5],[8]] => 0
[[1,2,6],[3,7],[4],[5],[8]] => 10
[[1,4,5],[2,7],[3],[6],[8]] => 4
[[1,3,5],[2,7],[4],[6],[8]] => 0
[[1,2,5],[3,7],[4],[6],[8]] => 13
[[1,3,4],[2,7],[5],[6],[8]] => 0
[[1,2,4],[3,7],[5],[6],[8]] => 10
[[1,2,3],[4,7],[5],[6],[8]] => 17
[[1,4,6],[2,5],[3],[7],[8]] => 4
[[1,3,6],[2,5],[4],[7],[8]] => 0
[[1,2,6],[3,5],[4],[7],[8]] => 11
[[1,3,6],[2,4],[5],[7],[8]] => 0
[[1,2,6],[3,4],[5],[7],[8]] => 8
[[1,4,5],[2,6],[3],[7],[8]] => 4
[[1,3,5],[2,6],[4],[7],[8]] => 0
[[1,2,5],[3,6],[4],[7],[8]] => 13
[[1,3,4],[2,6],[5],[7],[8]] => 0
[[1,2,4],[3,6],[5],[7],[8]] => 10
[[1,2,3],[4,6],[5],[7],[8]] => 19
[[1,3,5],[2,4],[6],[7],[8]] => 0
[[1,2,5],[3,4],[6],[7],[8]] => 8
[[1,3,4],[2,5],[6],[7],[8]] => 0
[[1,2,4],[3,5],[6],[7],[8]] => 10
[[1,2,3],[4,5],[6],[7],[8]] => 17
[[1,7,8],[2],[3],[4],[5],[6]] => 0
[[1,6,8],[2],[3],[4],[5],[7]] => 3
[[1,5,8],[2],[3],[4],[6],[7]] => 0
[[1,4,8],[2],[3],[5],[6],[7]] => 3
[[1,3,8],[2],[4],[5],[6],[7]] => 0
[[1,2,8],[3],[4],[5],[6],[7]] => 10
[[1,6,7],[2],[3],[4],[5],[8]] => 3
[[1,5,7],[2],[3],[4],[6],[8]] => 0
[[1,4,7],[2],[3],[5],[6],[8]] => 3
[[1,3,7],[2],[4],[5],[6],[8]] => 0
[[1,2,7],[3],[4],[5],[6],[8]] => 12
[[1,5,6],[2],[3],[4],[7],[8]] => 0
[[1,4,6],[2],[3],[5],[7],[8]] => 3
[[1,3,6],[2],[4],[5],[7],[8]] => 0
[[1,2,6],[3],[4],[5],[7],[8]] => 10
[[1,4,5],[2],[3],[6],[7],[8]] => 3
[[1,3,5],[2],[4],[6],[7],[8]] => 0
[[1,2,5],[3],[4],[6],[7],[8]] => 12
[[1,3,4],[2],[5],[6],[7],[8]] => 0
[[1,2,4],[3],[5],[6],[7],[8]] => 10
[[1,2,3],[4],[5],[6],[7],[8]] => 18
[[1,5],[2,6],[3,7],[4,8]] => 0
[[1,4],[2,6],[3,7],[5,8]] => 6
[[1,3],[2,6],[4,7],[5,8]] => 0
[[1,2],[3,6],[4,7],[5,8]] => 6
[[1,4],[2,5],[3,7],[6,8]] => 6
[[1,3],[2,5],[4,7],[6,8]] => 0
[[1,2],[3,5],[4,7],[6,8]] => 10
[[1,3],[2,4],[5,7],[6,8]] => 0
[[1,2],[3,4],[5,7],[6,8]] => 6
[[1,4],[2,5],[3,6],[7,8]] => 6
[[1,3],[2,5],[4,6],[7,8]] => 0
[[1,2],[3,5],[4,6],[7,8]] => 10
[[1,3],[2,4],[5,6],[7,8]] => 0
[[1,2],[3,4],[5,6],[7,8]] => 6
[[1,6],[2,7],[3,8],[4],[5]] => 4
[[1,5],[2,7],[3,8],[4],[6]] => 0
[[1,4],[2,7],[3,8],[5],[6]] => 4
[[1,3],[2,7],[4,8],[5],[6]] => 0
[[1,2],[3,7],[4,8],[5],[6]] => 10
[[1,5],[2,6],[3,8],[4],[7]] => 0
[[1,4],[2,6],[3,8],[5],[7]] => 4
[[1,3],[2,6],[4,8],[5],[7]] => 0
[[1,2],[3,6],[4,8],[5],[7]] => 7
[[1,4],[2,5],[3,8],[6],[7]] => 4
[[1,3],[2,5],[4,8],[6],[7]] => 0
[[1,2],[3,5],[4,8],[6],[7]] => 10
[[1,3],[2,4],[5,8],[6],[7]] => 0
[[1,2],[3,4],[5,8],[6],[7]] => 7
[[1,5],[2,6],[3,7],[4],[8]] => 0
[[1,4],[2,6],[3,7],[5],[8]] => 4
[[1,3],[2,6],[4,7],[5],[8]] => 0
[[1,2],[3,6],[4,7],[5],[8]] => 7
[[1,4],[2,5],[3,7],[6],[8]] => 4
[[1,3],[2,5],[4,7],[6],[8]] => 0
[[1,2],[3,5],[4,7],[6],[8]] => 10
[[1,3],[2,4],[5,7],[6],[8]] => 0
[[1,2],[3,4],[5,7],[6],[8]] => 7
[[1,4],[2,5],[3,6],[7],[8]] => 7
[[1,3],[2,5],[4,6],[7],[8]] => 0
[[1,2],[3,5],[4,6],[7],[8]] => 10
[[1,3],[2,4],[5,6],[7],[8]] => 0
[[1,2],[3,4],[5,6],[7],[8]] => 7
[[1,7],[2,8],[3],[4],[5],[6]] => 0
[[1,6],[2,8],[3],[4],[5],[7]] => 3
[[1,5],[2,8],[3],[4],[6],[7]] => 0
[[1,4],[2,8],[3],[5],[6],[7]] => 3
[[1,3],[2,8],[4],[5],[6],[7]] => 0
[[1,2],[3,8],[4],[5],[6],[7]] => 8
[[1,6],[2,7],[3],[4],[5],[8]] => 3
[[1,5],[2,7],[3],[4],[6],[8]] => 0
[[1,4],[2,7],[3],[5],[6],[8]] => 3
[[1,3],[2,7],[4],[5],[6],[8]] => 0
[[1,2],[3,7],[4],[5],[6],[8]] => 10
[[1,5],[2,6],[3],[4],[7],[8]] => 0
[[1,4],[2,6],[3],[5],[7],[8]] => 3
[[1,3],[2,6],[4],[5],[7],[8]] => 0
[[1,2],[3,6],[4],[5],[7],[8]] => 8
[[1,4],[2,5],[3],[6],[7],[8]] => 3
[[1,3],[2,5],[4],[6],[7],[8]] => 0
[[1,2],[3,5],[4],[6],[7],[8]] => 10
[[1,3],[2,4],[5],[6],[7],[8]] => 0
[[1,2],[3,4],[5],[6],[7],[8]] => 8
[[1,8],[2],[3],[4],[5],[6],[7]] => 2
[[1,7],[2],[3],[4],[5],[6],[8]] => 0
[[1,6],[2],[3],[4],[5],[7],[8]] => 2
[[1,5],[2],[3],[4],[6],[7],[8]] => 0
[[1,4],[2],[3],[5],[6],[7],[8]] => 2
[[1,3],[2],[4],[5],[6],[7],[8]] => 0
[[1,2],[3],[4],[5],[6],[7],[8]] => 10
[[1],[2],[3],[4],[5],[6],[7],[8]] => 0
[[1,2,3,4,5,6,7,8,9]] => 81
[[1,2,3,4,5,6,7,8],[9]] => 70
[[1,2,3,4,5,6,7],[8,9]] => 59
[[1,2,3,4,5,6,7],[8],[9]] => 61
[[1,3,4,5,6,7,8,9],[2]] => 0
[[1,2,5,6,7,8,9],[3,4]] => 9
[[1,4,5,6,7,8,9],[2],[3]] => 7
[[1,2,3,7,8,9],[4,5,6]] => 18
[[1,3,5,7,8,9],[2,4,6]] => 0
[[1,3,5,6,7,8,9],[2,4]] => 0
[[1,2,3,4,5,6,8],[7,9]] => 55
[[1,2,3,4,5,6,7,9],[8]] => 66
[[1,2,3,4,5,6,9],[7,8]] => 53
[[1,2,3,4,5,6,9],[7],[8]] => 57
[[1,2,4,5,6,7,8,9],[3]] => 16
[[1,3,4,6,7,8,9],[2,5]] => 0
[[1,3,5,6,7,8,9],[2],[4]] => 0
[[1,3,5,6,8,9],[2,4,7]] => 0
[[1,3,4,5,6,7,8],[2,9]] => 0
[[1,3,4,5,6,7,8],[2],[9]] => 0
[[1,2,3,6,7,8,9],[4,5]] => 23
[[1,2,5,6,7,8,9],[3],[4]] => 21
[[1,2,3,4,8,9],[5,6,7]] => 30
[[1,2,3,4,7,8,9],[5,6]] => 35
[[1,2,3,4,5,6,8],[7],[9]] => 55
[[1,2,3,5,7,9],[4,6,8]] => 26
[[1,2,3,4,5,7,9],[6,8]] => 48
[[1,2,4,6,8,9],[3,5,7]] => 14
[[1,2,4,6,7,8,9],[3,5]] => 15
[[1,2,4,5,6,7,8],[3,9]] => 15
[[1,3,4,5,7,9],[2,6,8]] => 0
[[1,3,4,5,6,7,9],[2,8]] => 0
[[1,2,3,5,6,7,8,9],[4]] => 30
[[1,2,4,5,7,8,9],[3,6]] => 15
[[1,2,4,6,7,8,9],[3],[5]] => 15
[[1,2,4,6,7,9],[3,5,8]] => 14
[[1,2,3,5,6,7,8],[4,9]] => 28
[[1,2,4,5,6,7,8],[3],[9]] => 15
[[1,2,3,4,5,6,8,9],[7]] => 60
[[1,2,3,4,5,7,8,9],[6]] => 52
[[1,2,3,4,6,7,8,9],[5]] => 42
[[1,2,3,4,5,8,9],[6,7]] => 45
[[1,2,3,4,5,8,9],[6],[7]] => 51
[[1,2,3,4,7,8,9],[5],[6]] => 43
[[1,2,3,6,7,8,9],[4],[5]] => 33
[[1,3,4,7,8,9],[2,5,6]] => 0
[[1,3,4,5,7,8,9],[2,6]] => 0
[[1,3,4,6,7,8,9],[2],[5]] => 0
[[1,3,5,6,7,9],[2,4,8]] => 0
[[1,2,3,4,5,7,8],[6],[9]] => 48
[[1,2,3,4,6,7,8],[5],[9]] => 39
[[1,2,3,5,6,7,8],[4],[9]] => 28
[[1,2,3,4,5,7,8],[6,9]] => 48
[[1,3,4,5,6,8,9],[2,7]] => 0
[[1,2,3,4,6,7,8],[5,9]] => 39
[[1,2,5,7,8,9],[3,4,6]] => 10
[[1,3,4,5,6,7,9],[2],[8]] => 0
[[1,3,4,5,6,8,9],[2],[7]] => 0
[[1,3,4,5,8,9],[2,6,7]] => 0
[[1,2,3,5,7,8,9],[4,6]] => 28
[[1,3,4,5,7,8,9],[2],[6]] => 0
[[1,2,3,6,8,9],[4,5,7]] => 23
[[1,2,3,4,6,8,9],[5,7]] => 39
[[1,2,4,7,8,9],[3,5,6]] => 10
[[1,2,3,4,5,7,9],[6],[8]] => 48
[[1,2,3,5,8,9],[4,6,7]] => 23
[[1,2,4,5,6,7,9],[3],[8]] => 15
[[1,2,3,4,6,8,9],[5],[7]] => 39
[[1,2,5,6,8,9],[3,4,7]] => 10
[[1,2,5,6,7,9],[3,4,8]] => 10
[[1,2,3,4,6,7,9],[5],[8]] => 39
[[1,2,3,5,6,7,9],[4,8]] => 28
[[1,2,3,5,6,8,9],[4,7]] => 28
[[1,2,3,4,6,7,9],[5,8]] => 39
[[1,2,4,5,8,9],[3,6,7]] => 14
[[1,2,4,5,6,7,9],[3,8]] => 15
[[1,2,4,5,7,9],[3,6,8]] => 14
[[1,2,3,5,6,8,9],[4],[7]] => 28
[[1,2,4,5,7,8,9],[3],[6]] => 15
[[1,2,3,5,7,8,9],[4],[6]] => 28
[[1,2,4,5,6,8,9],[3],[7]] => 15
[[1,3,4,6,7,9],[2,5,8]] => 0
[[1,3,4,6,8,9],[2,5,7]] => 0
[[1,2,4,5,6,8,9],[3,7]] => 15
[[1,2,3,6,7,9],[4,5,8]] => 23
[[1,2,3,5,6,7,9],[4],[8]] => 28
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Created: May 25, 2016 at 18:06 by Franco Saliola
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Last Updated: Mar 15, 2021 at 11:33 by Martin Rubey